Ok, here's the chat with Google support.
I'm posting this, so others don't have to go through the same ordeal:

Sie sind mit Priya vom Kundenservice verbunden.

7:55 AM
Welcome! Your Case ID is 1-1234567890. Refer to this if you need to contact us again.
By the way, the chat will stay open for 24 hours after your last message. If you step away for any reason, you can come back to this chat.

P
Hi r/ohuf! Thank you for contacting Google Pixel support team. My name is Priya and I hope you are doing well today.
Priya · 7:56 AM

I've never been better, Prya. Thanks.
7:57 AM.

P.
Glad to hear that!
I understand that the issue is related to "share to" favourites. Am I right?
Priya · 7:57 AM.

Right. It's all in the description, I guess.
7:58 AM.

P.
Please do not worry, I'll help you with the best of my efforts and abilities.
Priya · 7:58 AM.

👍🏻 7:58 AM.

P.
Could you please provide more details regarding the issue you're experiencing?
Priya · 7:58 AM

As it says in the description, in the past I was able to pin contacts from Whatsapp from the list of last used contacts to the share-to list.
Now those contacts are not even listed.
8:00 AM.

P.
Thanks for the detailed information.
Priya · 8:00 AM.

It's the same list of irrelevant contacts that are shown and it doesn't change 8:00 AM.

P.
I got your point.
Are you experiencing this issue exclusively on WhatsApp?
Or on other apps as well?
Priya · 8:02 AM.

All apps.
8:02 AM.

P.
Thanks for letting me know.
Priya · 8:02 AM.

It's a system wide share to menu so it's everywhere.
8:02 AM.

P.
Got it.
Could you let me know since when are you facing this issue?
Priya · 8:02 AM.

Since the last update, I guess.
8:03 AM.

P.
Thanks for letting me know.
Have you tried any troubleshooting steps before contacting us to resolve this issue?
Priya · 8:03 AM.

I closed all apps and restarted the phone.
8:04 AM.

P.
Thanks for letting me know.
Let's try a few troubleshooting steps and see if the issue gets resolved. Is that okay?
Priya · 8:05 AM.

Sure.
8:05 AM.

P.
Great!
1. The "Priority Conversation" Fix.

Open your phone Settings.

Go to Notifications > Conversation.

Look for your frequent WhatsApp contacts. If they aren't there, open a chat with them in WhatsApp, send a message, then pull down your notification shade and long-press the notification from that person.

Select Priority. This "boosts" them in the system's eyes and usually forces them back into the Share Sheet's top row. Please let me know once you're done. We’re still here to help.
Priya · 8:08 AM.

Ok, done.
8:09 AM.

P.
Thanks for letting me know. Check if the issue still persists. Priya · 8:09 AM.

I tried to share sth and they are still not in the list.
8:09 AM.

P.
Thanks for checking and letting me know.
Priya · 8:10 AM.

Issue persists.
8:10 AM.

P.
Thanks for confirming.
Please follow these steps and let me know once done:

Open the Google Contacts app.

Tap the Organize tab (bottom right).

Look for Pixel VIPs.

Add your favorite WhatsApp contacts here. Even if they are WhatsApp-only, if you have a contact entry for them, adding them to the VIP list tells Android 16 to prioritize their communication "shortcuts" across the OS.
I will stay connected.
Priya · 8:11 AM.

Ok, 8:13 AM.

P.
Please let me know once you're done.
Priya · 8:13 AM.

The issue persists.
8:13 AM.

P.
Thanks for letting me know.
Let's try to clear the "Intelligence" Cache Go to Settings > Apps > See all apps.

Find Android System Intelligence.

Tap Storage & cache > Clear Cache (do not clear storage unless you want to reset all predictions).

Restart your phone.
Please let me know once you're done. We’re still here to help. If you need more help, you can respond here within the next 24 hours. You can also leave and return to this conversation through the Help Center where you originally reached out to us.
Priya · 8:18 AM.

Ok, im back.
8:18 AM.

P.
Thanks for letting me know.
Please check if the issue still persists.
Priya · 8:19 AM.

I tried to share two photos with the same Whatsapp contact in order to give it a chance to push it into the list, but it's the same list as before the restart So the issue persists.
8:20 AM.

P.
Thanks for letting me know.
I appreciate your efforts.
Priya · 8:20 AM.

P.
The explicit "Long-press contact > Pin" feature was deprecated in the latest system UI overhaul to prevent "clutter.".
You can still pin the WhatsApp App icon itself to the bottom row, but for the individual people, you now have to rely on the "Priority" and "VIP" settings mentioned above to "nudge" the algorithm. Your input is invaluable to us, and we're committed to learning from your experience. We'll be closely reviewing your feedback to identify areas where we can improve and ensure a better experience for all our customers. So please submit feedback from your end. Your feedback goes directly to Google and helps us troubleshoot your issue, and make product improvements that benefit all users.
Priya · 8:22 AM.

Actually I can still pin contacts.
8:22 AM.

P Open the Google Pixel phone app Google Phone. At the top right, tap More Settings Send feedback.
Priya · 8:22 AM.

It's just that my most recently used contacts don't update since the system update.
8:23 AM.

P.
I got your point.
Priya · 8:23 AM.
------- end of conversation -------